@wvmarle, thank you for the information. Briefly on some points:
I take it you want to use PWM? There’s no such thing as a DAC in an ATtiny.
Yes, I am using PWM, achieving gradually changes in voltage on pin PB0.
Those 10µF caps C2 and C3 on the base of the transistors have to go. Instead you have to use a current limiting resistor - 330-470Ω for each.
Got it. By using capacitors I was planning to smooth the signal to prevent flickering of diodes.
No current limiting resistor on in series with the LEDs. You’ll burn your transistors this way.
Initially there were resistors between VCC (+9V) and LEDs, but because of the reliability of DC-DC converter is high I decided to cut them off. If it’s still necessary, I’ll add them back to scheme.
Two different part numbers for the transistors, that’s odd.
Indeed, there are two different transistors (P / N-type)
What is the purpose of R2 and D1? Get rid of them. 5V direct to the Vcc pin.
Because I can not rely to external power source and cannot change that as well, I decided to add voltage divider using R2-D1 joint. If that is not necessary, I will exclude them from circuit.
You miss a 100nF decoupling capacitor for the ATtiny.
Agreed, thanks
C1 also doesn’t seem to have any use.
Agreed
No ISP header (or how do you plan to program the thing?)
The reset pin is kept floating. Should have a pull-up, maybe a switch to GND if you want to be able to reset it.
The ISP header I decided to leave it for later, because there is a problem uploading firmware while the MCU is wired. My guess is that there should be some jumpers or a wiring trick to be able to isolate the ATTINY from the circuit while uploading. So, since we are touching the topic, any suggestions are welcome. 
ChrisTenone:
No, arduino.cc is not as busy as other electronic fora you may be familiar with. It’s a good idea to give it 24 hours before bumping.
Agreed.
@GoForSmoke, that is the lack of reliability of an external power source that I’ve mentioned above. So I wanted to use R2-D1 voltage regulator/divider. If that is a bad practice, I will remove them.
MCU is doing its job well, since I am able to dimm out the leds on one side meanwhile the leds on another size are turning high, and vise versa. I’m gonna take some time to redraw the schematics, re-wire all over again and calculate some values for resistors for debugging purposes.
Will be back in a short while.
Thanks to everyone~
--------------------------------------------- UPD:
@wvmarle schematic is attached, I hope that is close to a fine results now :). Please do criticize it, that helps a lot